Where Can I Find Generators of R4?

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Discussion Overview

The discussion revolves around the search for generators of the group of rotations in four-dimensional space (R^4), focusing on the mathematical and physical interpretations of this concept. Participants explore the nature of these generators and clarify their specific needs regarding the dimensionality of the group.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant inquires about the location of generators for the group of rotations in R^4.
  • Another participant notes that the group of all rotations in R^4 has an uncountable set of generators, suggesting that this may not be what the inquirer is looking for.
  • A later reply clarifies that the inquirer only needed a set of six generators that can generate the entire group, specifically mentioning rotations "around planes" rather than axes.
  • One participant highlights a potential miscommunication between pure mathematicians and theoretical physicists regarding the term "generators of the group," indicating that the inquirer may be seeking a basis for the 6-dimensional Lie algebra associated with the Lie group of rotations in R^4.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of "generators of the group," with some emphasizing the uncountable nature of the generators while others focus on the specific need for a finite set. The discussion remains unresolved regarding the precise definition and requirements for the generators.

Contextual Notes

There is a lack of clarity regarding the definitions used by participants, particularly between mathematical and physical contexts. The discussion does not resolve the implications of these differing definitions.

kaksmet
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Hey

Does anyone know where I can find the generators of the group of rotations in four dimensions?

thanks!
 
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The group of all rotation of R^4? That has an uncountable set of generators - I don't think you want to find those.
 
only needed a set of six that did generate the entire group. Found them, rotations "around planes" instead of around axes. thanks anyway.
 
matt grime said:
The group of all rotation of R^4? That has an uncountable set of generators - I don't think you want to find those.

This is an example of miscommunication between pure mathematicians and theoretical physicists, for whom the term "generators of the group" means quite different things.

Here, I think kaksmet was looking for a basis for the 6-dimensional Lie algebra of the Lie group of rotations on R^4.
 

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